This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigor… Mehr…
This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory.The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics.Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered.This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods.The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero- dynamics.This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980).The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s.Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest.In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.; PDF; Scientific, Technical and Medical > Physics > Classical mechanics, Springer Berlin Heidelberg<
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This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigor… Mehr…
This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use., Springer<
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This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigor… Mehr…
This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory.The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics.Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered.This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods.The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero- dynamics.This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980).The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s.Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest.In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use.; PDF; Scientific, Technical and Medical > Physics > Classical mechanics, Springer Berlin Heidelberg<
No. 9783642841088. Versandkosten:Instock, Despatched same working day before 3pm, zzgl. Versandkosten.
This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigor… Mehr…
This is a book about spectral methods for partial differential equations: when to use them, how to implement them, and what can be learned from their of spectral methods has evolved rigorous theory. The computational side vigorously since the early 1970s, especially in computationally intensive of the more spectacular applications are applications in fluid dynamics. Some of the power of these discussed here, first in general terms as examples of the methods have been methods and later in great detail after the specifics covered. This book pays special attention to those algorithmic details which are essential to successful implementation of spectral methods. The focus is on algorithms for fluid dynamical problems in transition, turbulence, and aero dynamics. This book does not address specific applications in meteorology, partly because of the lack of experience of the authors in this field and partly because of the coverage provided by Haltiner and Williams (1980). The success of spectral methods in practical computations has led to an increasing interest in their theoretical aspects, especially since the mid-1970s. Although the theory does not yet cover the complete spectrum of applications, the analytical techniques which have been developed in recent years have facilitated the examination of an increasing number of problems of practical interest. In this book we present a unified theory of the mathematical analysis of spectral methods and apply it to many of the algorithms in current use., Springer<
Nr. 978-3-642-84108-8. Versandkosten:Worldwide free shipping, , DE. (EUR 0.00)
*Spectral Methods in Fluid Dynamics* / pdf eBook für 90.99 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Wissenschaften, allgemein Medien > Bücher nein eBook als pdf eBooks > Fa… Mehr…
*Spectral Methods in Fluid Dynamics* / pdf eBook für 90.99 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Wissenschaften, allgemein Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Wissenschaften allgemein, Springer Berlin Heidelberg<
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Detailangaben zum Buch - Spectral Methods in Fluid Dynamics
EAN (ISBN-13): 9783642841088 Erscheinungsjahr: 2012 Herausgeber: Springer Berlin Heidelberg
Buch in der Datenbank seit 2017-04-25T07:49:16+02:00 (Berlin) Detailseite zuletzt geändert am 2023-10-11T12:23:40+02:00 (Berlin) ISBN/EAN: 9783642841088
ISBN - alternative Schreibweisen: 978-3-642-84108-8 Alternative Schreibweisen und verwandte Suchbegriffe: Autor des Buches: canuto claudio, quarteroni alfio Titel des Buches: spectral methods, fluid dynamics
Daten vom Verlag:
Autor/in: Claudio Canuto; M.Yousuff Hussaini; Alfio Quarteroni; Thomas A., Jr. Zang Titel: Scientific Computation; Spectral Methods in Fluid Dynamics Verlag: Springer; Springer Berlin 568 Seiten Erscheinungsjahr: 2012-12-06 Berlin; Heidelberg; DE Sprache: Englisch 96,29 € (DE) 99,00 € (AT) 106,50 CHF (CH) Available XVI, 568 p. 6 illus.
1. Introduction.- 1.1. Historical Background.- 1.2. Some Examples of Spectral Methods.- 1.3. The Equations of Fluid Dynamics.- 1.4. Spectral Accuracy for a Two-Dimensional Fluid Calculation.- 1.5. Three-Dimensional Applications in Fluids.- 2. Spectral Approximation.- 2.1. The Fourier System.- 2.2. Orthogonal Polynomials in ( — 1, 1).- 2.3. Legendre Polynomials.- 2.4. Chebyshev Polynomials.- 2.5. Generalizations.- 3. Fundamentals of Spectral Methods for PDEs.- 3.1. Spectral Projection of the Burgers Equation.- 3.2. Convolution Sums.- 3.3. Boundary Conditions.- 3.4. Coordinate Singularities.- 3.5. Two-Dimensional Mapping.- 4. Temporal Discretization.- 4.1. Introduction.- 4.2. The Eigenvalues of Basic Spectral Operators.- 4.3. Some Standard Schemes.- 4.4. Special Purpose Schemes.- 4.5. Conservation Forms.- 4.6. Aliasing.- 5. Solution Techniques for Implicit Spectral Equations.- 5.1. Direct Methods.- 5.2. Fundamentals of Iterative Methods.- 5.3. Conventional Iterative Methods.- 5.4. Multidimensional Preconditioning.- 5.5. Spectral Multigrid Methods.- 5.6. A Semi-Implicit Method for the Navier—Stokes Equations.- 6. Simple Incompressible Flows.- 6.1. Burgers Equation.- 6.2. Shear Flow Past a Circle.- 6.3. Boundary-Layer Flows.- 6.4. Linear Stability.- 7. Some Algorithms for Unsteady Navier—Stokes Equations.- 7.1. Introduction.- 7.2. Homogeneous Flows.- 7.3. Inhomogeneous Flows.- 7.4. Flows with Multiple Inhomogeneous Directions.- 7.5. Mixed Spectral/Finite-Difference Methods.- 8. Compressible Flow.- 8.1. Introduction.- 8.2. Boundary Conditions for Hyperbolic Problems.- 8.3. Basic Results for Scalar Nonsmooth Problems.- 8.4. Homogeneous Turbulence.- 8.5. Shock-Capturing.- 8.6. Shock-Fitting.- 8.7. Reacting Flows.- 9. Global Approximation Results.- 9.1. FourierApproximation.- 9.2. Sturm—Liouville Expansions.- 9.3. Discrete Norms.- 9.4. Legendre Approximations.- 9.5. Chebyshev Approximations.- 9.6. Other Polynomial Approximations.- 9.7. Approximation Results in Several Dimensions.- 10. Theory of Stability and Convergence for Spectral Methods.- 10.1. The Three Examples Revisited.- 10.2. Towards a General Theory.- 10.3. General Formulation of Spectral Approximations to Linear Steady Problems.- 10.4. Galerkin, Collocation and Tau Methods.- 10.5. General Formulation of Spectral Approximations to Linear Evolution Equations.- 10.6. The Error Equation.- 11. Steady, Smooth Problems.- 11.1. The Poisson Equation.- 11.2. Advection-Diffusion Equation.- 11.3. Navier—Stokes Equations.- 11.4. The Eigenvalues of Some Spectral Operators.- 12. Transient, Smooth Problems.- 12.1. Linear Hyperbolic Equations.- 12.2. Heat Equation.- 12.3. Advection-Diffusion Equation.- 13. Domain Decomposition Methods.- 13.1. Introduction.- 13.2. Patching Methods.- 13.3. Variational Methods.- 13.4. The Alternating Schwarz Method.- 13.5. Mathematical Aspects of Domain Decomposition Methods.- 13.6. Some Stability and Convergence Results.- Appendices.- A. Basic Mathematical Concepts.- B. Fast Fourier Transforms.- C. Jacobi—Gauss—Lobatto Roots.- References. This textbook presents the modern unified theory of spectral methods and their implementation in the numerical analysis of partial differential equations occuring in fluid dynamical problems of transition, turbulence, and aerodynamics. The book addresses graduate students and researchers in fluid dynamics and applied mathematics as well as engineers working on problems of practical importance.
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